biomechanics - angular kinematics

Question

While bowling a cricket ball, Carl Spackler holds the ball 0.9m from the axis of rotation at his shoulder. The movement takes 0.42s and, at the moment of release, the ball has a tangential linear velocity of 40m/s and an angular acceleration of 120rad/s2.

a) What are the magnitudes of the tangential and centripetal accelerations at release?

b) What is the magnitude of the resultant acceleration of the ball?

Answer 1

The first step would be to identify the givens:

1. radius = 0.9 m
2. time = .42s
3. tangential liner velocity (VT) = 40 m/s
4. angular acceleration (alpha) = 120 r/s^2

Now we must remember which equations are relevant:

1. tangential acceleration (AT) = alpha * r
2. centripetal acceleration = v^2 / r = angular velocity (w) / r

a) AT = alpha * r

AT = 120 * .9

AT = 108

*something to important to remember here is that we are comparing linear values (AT) to angular values (alpha) so we have to make sure that our units are in radians and not degrees. The givens were given to us in radians for this problem, but if they were in degrees/sec then we would have to convert using pi rad / 180 degree

centripetal acceleration = v^2 / r

* Centripetal acceleration has 2 possible equations (shown above in the equation section. use the equation that has 1) the unknown value in it 2) the most givens from the initial question in it.

centripetal acceleration = v^2 / r

centripetal acceleration = 40^2 /.9

centripetal acceleration = 1,777.7

* If you are asked to draw centripetal acceleration make sure that it is always pointing toward the axis of rotation. Also, in the problem it says "at the moment of release", make sure that you are using the correct values. For example, if the problem gave an initial and final value, you would want to use the final value because that is the value that represents "at release".

I hope this helps you. Let me know if I can be of further assistance.